I asked myself this question with every series and now I've settled on some MODs I feel are safe to use.

I consider MODs those packages that change or enhance "the stuff in the background".
I consider CC (Custom Content) those items that have been created and are visible in the game. There is official CC and unofficial (aka user-created) CC.

My favourite MODs for the Sims 3 have been several of NRAAS. While some MODs achieve the same, using only one "system" seems to cause the least amount of problems.
From NRAAS I use:
- Overwatch: "This mod's purview is the correction of persistent or recurring errors produced by the Core game or other mods." (stated on the website) It sounds simple, but it actually does loads if you want to. For the full features and options see: http://nraas.wikispaces.com/Overwatch+FAQ I use this mod with the default settings/options.
- Master Controller: "The mod contains interactions for managing the entire population of your town. However, unlike other mods in my suite, there is no automated component to this mod. All changes must be performed manually by selecting the appropriate interaction. This ensures that the mod does not interfere with any aspect of the game without your explicit direction." Use this in combination with the Story Progression mod with the immigrant balance to fill your town optimally with NPCs. You can also use this MOD to switch households in your town! See also: http://nraas.wikispaces.com/MasterController
- Story Progression: "Unlike The Sims 2, where a single household was simulated at any one time. The Sims 3 simulates an entire town of sims all at the same time. However since only one household can be actively controlled by you at any one time, something needs to control the rest of the sims in town. This is where Story Progression comes into play. It pushes the inactive sims to get jobs, make friends, get married, have children, and generally get on with their virtual lives." This does the job a lot better than EA and has several modules to enhance it to your liking. I use this together with the Master Controller to see other households progress or mine (after switching back and forth). See also: http://nraas.wikispaces.com/StoryProgression
- Relativity: This allows you to change the in-game time speed. That is, the speed of the clock. I've set mine a little slower, so my in-game days take longer Real Time to finish. http://nraas.wikispaces.com/Relativity
- Traveler: This mod ensures correction of several potentially lost details about your Sim and their inventory at transition when travelling to either other lands, university or the future. No need to configure it. See: http://nraas.wikispaces.com/Traveler+FAQ

One of these MODs (I guess Overwatch or Master Controller) also unsticks townies (both Sims and Animals) and cleans up vehicles, turns off left on TVs (from Townies) and checks a whole bunch of other things at 3am IGT (In-Game Time). They both have loads of things you can tweak if desired to make the game different.

I also use many of NRAAS' mods as well as skins, a mod that gives your family higher starting out incomes, and the plantastic mod from Twoftmama's Naughty Sim Asylum. The plantastic mod comes with a variety of options, depending on how you want your gardening efforts rewarded. The mod that adjusts starting funds also has several sub-mods from which to choose. I forgot the name of the family funds mod and don't have access to my password to the site at the moment, but it also adjusts the income level needed for a family to be considered "rich," if I am remembering correctly.

I'm definitely not ready to install a mod yet, but reading about how the game works, I realized that I'm gonna have to rethink how I'm playing. I know that if you switch households, the ones that you just switched from could move out of town just like the other Sims that I'm not controlling. So, I just wanted to make sure, but the only way I'm gonna be able to add Sims that I make to the town without any of them moving out, would be to use a mod? I don't know if this would work, but since I'm only in control of one family at a time, I was wanting the townies to be Sims that I make instead of the ones the game makes. But, game townies would be fine as long as the ones I made don't move out. I just don't see the point in being able to make all these different Sims if they can just move out of town, cause it takes time when you can customize Sims the way you can in this game.

@KissieK, that is how I'm playing too. I've deleted most of the regular townies and have made my own families. I give them jobs and skills to work on then switch to another family. To keep them from moving out of town or changing jobs, go into options and turn off story progression. I actually love this because while the sim I'm playing is out and about she sees them. It's nice seeing them around going about their business!

i play The Sims 3 now and then but this these are my favorie hands down
Grim's The Sims 3 Auto Save- It automatically saves your game
Nras- as everybody
and almost if not everything by user Treeg
The Sims 3 Dashboard- Great for checking out what is wrong with CC

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